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A Sparse Latent Class Model for Cognitive Diagnosis

Published online by Cambridge University Press:  01 January 2025

Yinyin Chen ,
Steven Culpepper Open the ORCID record for Steven Culpepper [Opens in a new window]  and
Feng Liang
Yinyin Chen
Affiliation:
University of Illinois at Urbana–Champaign
Steven Culpepper*
Affiliation:
University of Illinois at Urbana–Champaign
Feng Liang
Affiliation:
University of Illinois at Urbana–Champaign
*
Correspondence should be made to Steven Culpepper, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana–Champaign, 725 South Wright Street, Champaign, IL 61820, USA. Email: sculpepp@illinois.edu
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Abstract

Cognitive diagnostic models (CDMs) are latent variable models developed to infer latent skills, knowledge, or personalities that underlie responses to educational, psychological, and social science tests and measures. Recent research focused on theory and methods for using sparse latent class models (SLCMs) in an exploratory fashion to infer the latent processes and structure underlying responses. We report new theoretical results about sufficient conditions for generic identifiability of SLCM parameters. An important contribution for practice is that our new generic identifiability conditions are more likely to be satisfied in empirical applications than existing conditions that ensure strict identifiability. Learning the underlying latent structure can be formulated as a variable selection problem. We develop a new Bayesian variable selection algorithm that explicitly enforces generic identifiability conditions and monotonicity of item response functions to ensure valid posterior inference. We present Monte Carlo simulation results to support accurate inferences and discuss the implications of our findings for future SLCM research and educational testing.

Keywords

sparse latent class modelsBayesian variable selectionidentifiability
Type
Theory and Methods
Information
Psychometrika , Volume 85 , Issue 1 , March 2020 , pp. 121 - 153
Copyright
Copyright © 2020 The Psychometric Society

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